Costly Contracts and Consumer Credit by Igor Livshits, James MacGee and Michèle Tertilt Working Paper # 2011-1 June 2011 Economic Policy Research Institute EPRI Working Paper Series Department of Economics Department of Political Science Social Science Centre The University of Western Ontario London, Ontario, N6A 5C2 Canada This working paper is available as a downloadable pdf file on our website http://economics.uwo.ca/centres/epri/ Costly Contracts and Consumer Credit∗ Igor Livshits James MacGee University of Western Ontario, BEROC University of Western Ontario Mich` le Tertilt e University of Mannheim, Stanford University, NBER and CEPR June 20, 2011 Abstract Financial innovations are a common explanation of the rise in consumer credit and bankruptcies To evaluate this story, we develop a simple model that incorporates two key frictions: asymmetric information about borrowers’ risk of default and a fixed cost to create each contract offered by lenders Innovations which reduce the fixed cost or ameliorate asymmetric information have large extensive margin effects via the entry of new lending contracts targeted at riskier borrowers This results in more defaults and borrowing, as well as increased dispersion of interest rates Using the Survey of Consumer Finance and interest rate data collected by the Board of Governors, we find evidence supporting these predictions, as the dispersion of credit card interest rates nearly tripled, and the share of credit card debt of lower income households nearly doubled Keywords: Consumer Credit, Endogenous Financial Contracts, Bankruptcy JEL Classifications: E21, E49, G18, K35 Corresponding Author: Mich` le Tertilt, Department of Economics, University of Mannheim, Gere many, e-mail: tertilt@uni-mannheim.de We thank Kartik Athreya and Richard Rogerson as well as seminar participants at Alberta, Arizona State, British Columbia, Brock, Carleton, NYU, Pennsylvania State, Rochester, Simon Fraser, UCSD, UCSB, USC, Windsor, Federal Reserve Bank of Richmond, Federal Reserve Bank of Cleveland, Stanford and Philadelphia Fed Bag Lunches, the 2007 Canadian Economic Association and Society for Economic Dynamics, and the 2008 American Economic Association Annual meetings for helpful comments We are especially grateful to Karen Pence for her assistance with the Board of Governors interest rate data We thank the Economic Policy Research Institute, the Social Science and Humanities Research Council (Livshits, MacGee) and the National Science Foundation SES-0748889 (Tertilt) for financial support Wendi Goh, Vuong Nguyen, and Alex Wu provided excellent research assistance MacGee thanks the Federal Reserve Bank of Cleveland for their support during the writing of this paper The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Cleveland or the Federal Reserve System ∗ Introduction Financial innovations are frequently cited as playing an essential role in the dramatic rise in credit card borrowing over the past thirty years By making intensive use of improved information technology, it is argued that lenders were able to more accurately price risk and to offer loans more closely tailored to the risk characteristics of different groups (Mann 2006; Baird 2007) This dramatic expansion in credit card borrowing, in turn, is thought to be a key force driving the surge in consumer bankruptcy filings and unsecured borrowing (see Figure I) over the past thirty years (White 2007) Surprisingly little theoretical work, however, has explored the implications of financial innovations for unsecured consumer loans, or compared these predictions to the data We address this gap by developing a simple incomplete markets model of bankruptcy to analyze the qualitative implications of improved credit technology Further, to assess the model predictions, we assemble cross-sectional data on the evolution of credit card debt in the U.S from the early 1980s to the mid 2000s Our model incorporates two frictions which play a key role in shaping credit contracts: asymmetric information about borrowers’ default risk and a fixed cost to create a credit contract While asymmetric information is a common element of credit market models, fixed costs of contract design have been largely ignored by the academic literature.1 This is surprising, as texts targeted at practitioners discuss significant fixed costs associated with consumer credit contracts According to Lawrence and Solomon (2002), a prominent consumer credit handbook, the development of a consumer lending product involves selecting the target market, researching the competition, designing the terms and conditions of the product, (potentially) testing the product, forecasting profitability, preparing formal documentation, as well as an annual review of the product Even after the initial launch, there are additional overhead costs, such as customer data base maintenance, that vary little with the number of customers.2 Finally, it is worth noting that fixed costs are consistent with the observation that consumer credit contracts are differentiated but rarely individual specific Notable exceptions to this are Allard, Cresta, and Rochet (1997) and Newhouse (1996), who show that fixed costs can support pooling equilibria in insurance markets with a finite number of risk types A similar process is described in other guidebooks For example, Siddiqi (2006), outlines the development process of credit risk scorecards which map individual characteristics (for a particular demographic group) into a risk score Large issuers develop their own “custom scorecards” based on customer data, while some firms use purchased data Because of changes to the economic environment, scorecards are frequently updated, so there is not one “true” risk mapping that once developed is a public good We incorporate these frictions into a two-period model that builds on the classic contribution of Jaffee and Russell (1976) The economy is populated by a continuum of two-period lived risk-neutral borrowers Borrowers differ in their probabilities of receiving a high endowment realization in the second period To offer a lending contract, which specifies an interest rate, a borrowing limit and a set of eligible borrowers, an intermediary incurs a fixed cost When designing loan contracts, lenders face an asymmetric information problem, as they observe a noisy signal of a borrower’s true default risk, while borrowers know their type There is free entry into the credit market, and the number and terms of lending contracts are determined endogenously To address well known issues of existence of competitive equilibrium with adverse selection, the timing of the lending game builds on Hellwig (1987) This leads prospective lenders to internalize how their entry decisions impact other lenders’ entry and exit decisions The equilibrium features a finite set of loan contracts, each “targeting” a specific pool of risk types The finiteness of contracts follows from the assumption that a fixed cost is incurred per contract offered, so that some “pooling” is necessary to spread the fixed cost across multiple types of borrowers Working against larger pools is that bigger pools requires a broader range of risk types, which leads to larger gaps between the average default rate of the pool and the default risk of the least risky pool members With free entry of intermediaries, these two forces lead to a finite set of contracts for any (strictly positive) fixed cost We use this framework to analyze the qualitative implications of three financial innovations which may have had a significant impact on credit card lending over the past thirty years: (i) reductions in the fixed cost of creating contracts; (ii) increased accuracy of the lenders’ predictions of borrowers’ default risk (which mitigates adverse selection); and (iii) a reduced cost of lenders’ funds As we discuss in Section 1.1, the first two innovations capture the idea that better and cheaper information technology reduced the cost of designing financial contracts, and allowed lenders to more accurately price borrowers’ risk The third channel is motivated by the increased use of securitization (which reduced lenders’ costs of funds) as well as lower costs of servicing consumer loans as a result of improved information technology All three forms of financial innovation lead to significant changes in the extensive margin of who has access to risky loans The measure of households offered risky loans depends on both the number of risky contracts and the size of each pool Intuitively, financial innovation makes the lending technology more productive, which leads to it being used more intensively to sort borrowers into smaller pools Holding the number of contracts fixed, this reduces the number of households with risky borrowing However, improved lending technology makes the marginal contract more attractive to borrowers by lowering the break-even interest rate Thus, sufficiently large financial innovations lead to the entry of new contracts, targeted at riskier types than served by existing contracts In the model, the new contract margin dominates the local effect of smaller pools, so that new contracts lead to an increase in the number of borrowers Aggregate borrowing and defaults are driven by the extensive margin, with more borrowers leading to more borrowing and defaults Changes in the size and number of contracts induced by financial innovations result in more disperse interest rates, as rates for low risk borrowers decline, while high risk borrowers gain access to high rate loans Smaller pools lower the average gap between a household’s default risk and their interest rate, which leads to improved risk-based pricing This pricing effect is especially pronounced when the accuracy of the lending technology improves, as fewer high risk borrowers are misclassified as low risk One dimension along which improved risk assessment differs from the other innovations is the average default rate of borrowers On the one hand, whenever the number of contracts increases, households with riskier observable characteristics gain access to risky loans On the other hand, an increase in signal accuracy reduces the number of misclassified high risk types who are offered loans targeted at low risk borrowers, which acts to lower defaults In our numerical example, these two effects roughly offset each other, so that improved risk assessment leaves the average default rate of borrowers essentially unchanged To evaluate these predictions, we examine changes in the distribution of credit card debt and interest rates, using data from the Survey of Consumer Finance from 1983 to 2004 We find that the model predictions line up surprisingly well with trends in the credit card market Using credit card interest rates as a proxy for product variety, we find that the number of different contracts tripled between 1983 and 2001 Even more strikingly, the empirical density of credit card interest rates has become much “flatter” While nearly 55% of households in 1983 reported the same interest rate (18%), by the late 1990s no credit card rate was shared by more than 10% of households This has been accompanied by more accurate pricing of risk, as the relationship between observable risk factors (such as recent delinquencies) and interest rates has tightened since the early 1980s Finally, we find that the largest increase in access to credit cards has been for lower income households, whose share of total credit card debt more than doubled The model also provides novel insights into competition in consumer credit markets In an influential paper, Ausubel (1991) argued that the fact that declines in the risk-free rate during the 1980s did not lower average credit card rates was “ paradoxical within the paradigm of perfect competition.” In contrast, this episode is consistent with our competitive framework The extensive margin is key to understanding why our predictions differ from Ausubel (1991) A decline in the risk-free rate makes borrowing more attractive, encouraging entry of new loan contracts that target riskier borrowers This pushes up the average risk premium, increasing the average borrowing rate Thus, unlike in the standard competitive lending model, the effect of a lower risk-free rate on the average borrowing rate is ambiguous This extensive margin channel also provides insight into recent empirical work by Dick and Lehnert (2010) They find that increased competition, due to interstate bank deregulation, contributed to the rise in bankruptcies Our model suggests a theoretical mechanism that could account for this observation By lowering barriers to interstate banking, deregulation acts to expand market size, which effectively lowers the fixed cost of contracts In our framework, this leads to the extension of credit to riskier borrowers, resulting in more bankruptcies Our framework also has interesting implications for the debate over the welfare implications of financial innovations In our environment, while financial innovations increase average (ex ante) welfare, they are not Pareto improving, as changes in the size of each contract result in some households being pushed into higher interest rate contracts Moreover, the competitive equilibrium allocation is in general not efficient, as it features a greater product variety (more contracts) and less cross-subsidization than would be chosen by a social planner who weights all households equally As a result, in equilibrium more resources are consumed by the financial sector than is optimal This paper is related to the incomplete market framework of consumer bankruptcy of Chatterjee et al (2007) and Livshits, MacGee, and Tertilt (2007).3 Livshits, MacGee, and Tertilt (2010) and Athreya (2004) use this framework to quantitatively evaluate alternative explanations for the rise in bankruptcies and borrowing Both papers conclude that changes in consumer lending technology, rather than increased idiosyncratic risk (e.g., increased earnings volatility), are the main factors driving the rise in bankruptcies.4 Un3 Chatterjee, Corbae, and Rios-Rull (2010) and Chatterjee, Corbae, and Rios-Rull (2008) extend this work and formalize how credit histories and credit scoring support the repayment of unsecured credit Moss and Johnson (1999) argue, based on an analysis of borrowing trends, that the main cause of the rise in bankruptcies is an increase in the share of unsecured credit held by lower income households like our paper, they abstract from how financial innovations change equilibrium loan contracts and the pricing of borrowers default risk, and model financial innovation in an ad hoc way as a fall in the “stigma” of bankruptcy and lenders cost of funds Closely related in spirit is complementary work by Narajabad (2010), Sanchez (2010), Athreya, Tam, and Young (2008), and Drozd and Nosal (2008) Narajabad (2010), Sanchez (2010) and Athreya, Tam, and Young (2008) examine improvements in lenders’ ability to predict default risk In these papers, more accurate or cheaper signals lead to relatively lower risk households borrowing more (i.e., a shift in the intensive margin), which increases their probability of defaulting Drozd and Nosal (2008) examine a reduction in the fixed cost incurred by the lender to solicit potential borrowers, which leads to lower interest rates and increased competition for borrowers Our work differs from these papers in several key respects First, we introduce a novel mechanism which operates through the extensive rather than the intensive margin Second, our tractable framework allows us to analyze three different types of financial innovations, and provides interesting insight into the mechanisms linking lending environment and the degree of dispersion in credit contracts Our analysis also suggests new interpretations of “competition” in consumer credit markets, the Ausubel (1991) puzzle, and the effects of relaxing geographic restrictions to credit market competition Also related to this paper is recent work on competitive markets with adverse selection Adams, Einav, and Levin (2009), Einav, Jenkins, and Levin (2010) and Einav, Jenkins, and Levin (2009) find that subprime auto lenders face both moral hazard and adverse selection problems when designing the pricing and contract structure of auto loans, and that there are significant returns to improved technology to evaluate loan applicants (credit scoring) Earlier work by Ausubel (1999) also found that adverse selection is present in the credit card market Recent work by Dubey and Geanakoplos (2002), Guerrieri, Shimer, and Wright (2010) and Bisin and Gottardi (2006) considers existence and efficiency of competitive equilibria with adverse selection Our paper differs both in its focus on financial innovations, and incorporation of fixed costs of creating contracts The remainder of the paper is organized as follows Section 1.1 documents technological progress in the financial sector over the last couple decades, Section outlines the general model In Section we characterize the set of equilibrium contracts, while Section examines the implications of financial innovations Section compares these predictions to data on the evolution of credit card borrowing Section concludes 1.1 Financial Innovation It is frequently asserted that the past thirty years have witnessed the diffusion and introduction of numerous innovations in consumer credit markets (Mann 2006) Many of these changes are attributed to improved information technology, which has led to increased information sharing on borrowers between financial intermediaries (Barron and Staten 2003; Berger 2003; Evans and Schmalensee 1999) Here we briefly outline several important innovations in the credit card market (which largely accounts for the rise in unsecured consumer debt): the development and diffusion of improved credit-scoring techniques to identify and monitor creditworthy customers;5 increased use of computers to process information to facilitate customer acquisition, design credit card contracts, and monitor repayment; and the increased securitization of credit card debt.6 The development of automated credit scoring systems played an important role in the growth of the credit card industry (Evans and Schmalensee 1999; Johnson 1992) Credit scoring refers to the evaluation of the credit risk of loan applicants using historical data and statistical techniques (Mester 1997) Credit scoring technology figures centrally in credit card lending for two reasons First, it decreased the cost of evaluating loan applications (Mester 1997) Second, it led to increased analysis of the relationship between borrower characteristics and loan performance, and thus led to increased risk based pricing This resulted in substantial declines in interest rates for low risk customers and increased rates for higher risk consumers (Barron and Staten 2003).7 Improvements in computational technology led to credit scoring becoming widely used during the 1980s and 1990s (McCorkell 2002; Engen 2000; Asher 1994) The fraction of large banks using credit scoring as a loan approval criteria increased from half in 1988 to nearly seven-eights in 2000 Further, the fraction of large banks using fully automated loan processing (for direct loans) increased from 12 percent in 1988 to nearly 29 percent in 2000 (Installment Lending Report 2000) While larger banks are more likely than smaller banks to create their own credit scores, banks of any size have been using this technology by purchasing scores from other providers (Berger 2003) In fact, credit The most prominent is Fair Isaac Cooperation, the developer of the FICO score, who started building credit scoring systems in the late 1950s In 1975 Fair Isaac introduced the first behavior scoring system, and in 1981 introduced the Fair Isaac credit bureau scores See: http://en.wikipedia.org/wiki/Fair Isaac While references to financial innovation are common, few empirical studies attempt to quantitatively document its extent: “A striking feature of this literature [ ] is the relative dearth of empirical studies that [ ] provide a quantitative analysis of financial innovation.” (Frame and White (2004)) A similar finding holds for small business loans, where bank adoption of credit scoring led to the extension of credit to “marginal applicants” at higher interest rates (Berger, Frame, and Miller 2005) bureaus have increasingly collected information on borrowers and have been selling the information to lenders The number of credit reports issued has increased dramatically from 100 million in 1970 to 400 million in 1989, to more than 700 million today The information in these files is widely used by lenders (as an input into credit scoring), as more than two million credit reports are sold daily by U.S credit bureaus (Riestra 2002).8 The reduction in information processing costs may have also lowered the cost of designing and offering unsecured loan contracts As discussed earlier, deciding on the target market and terms of credit products is typically data intensive as it involves statistical analysis of large data sets In addition, the cost of maintaining and processing different loan products is also information intensive, so that improved information technology both reduced the fixed cost of maintaining differentiated credit products and lowered the cost of servicing each account There has also been significant innovations in how credit card companies finance their operations Beginning in 1987, credit card companies began to securitize credit card receivables Securitization increased rapidly, with over a quarter of bank credit card balances securitized by 1991, and nearly half by 2005 (Federal Reserve Board 2006) This has led to reduced financing costs for credit card lenders (Furletti 2002; Getter 2008) Model Environment We analyze a two-period small open economy populated by a continuum of borrowers, who face stochastic endowment in period Markets are incomplete as only noncontingent contracts can be issued However, borrowers can default on contracts by paying a bankruptcy cost Financial intermediaries can access funds at an (exogenous) risk-free interest rate r, incur a fixed cost to design each financial contract (characterized by a lending rate, a borrowing limit and eligibility requirement for borrowers) and observe a (potentially) noisy signal of borrowers’ risk types U.S credit bureaus report borrowers’ payment history, debt and public judgments (Hunt 2006) 2.1 People Borrowers live for two periods and are risk-neutral, with preferences represented by: c1 + βEc2 Each household receives the same deterministic endowment of y1 units of the consumption good in period The second period endowment, y2 , is stochastic taking one of two possible values: y2 ∈ {yh , yl }, where yh > yl Households differ in their probability ρ of receiving the high endowment yh We identify households with their type ρ, which is distributed uniformly on [0, 1].9 While each household knows their type, other agents observe a public signal, σ, regarding a household’s type With probability α, this signal is accurate: σ = ρ With probability (1 − α), the signal is an independent draw from the ρ distribution (U[0, 1]) Throughout the paper, we assume that β < q = ¯ , 1+r so that households always want to borrow at the risk-free rate Households’ borrowing, however, is limited by their inability to commit to repaying loans 2.2 Bankruptcy There is limited commitment by borrowers who can choose to declare bankruptcy in period The cost of bankruptcy to a borrower is the loss of fraction γ of the secondperiod endowment Lenders not recover any funds from defaulting borrowers 2.3 Financial Market Financial markets are competitive Financial intermediaries can borrow at the exogenously given interest rate r and make loans to borrowers Loans take the form of one period non-contingent bond contracts However, the bankruptcy option introduces a partial contingency by allowing bankrupts to discharge their debts Financial intermediaries incur a fixed cost χ to offer each non-contingent lending contract to (an unlimited number of) households Endowment-contingent contracts are The characterization of equilibria is practically unchanged for an arbitrary support [a, b] ⊆ [0, 1] 5.2.2 Increased Risk Based Pricing A second key prediction of all three financial innovations is that more contracts should be accompanied by better risk-based pricing To see whether interest rates more accurately reflect household risk, we compare the SCF distribution of interest rates for households who were delinquent on at least one debt payment in the past year to nondelinquents Delinquency on debt is positively correlated with the probability of future default, so delinquent households should be riskier than non-delinquents (Gross and Souleles 2002) The top panel of Figure VII shows that the distributions of interest rates for delinquents and non-delinquents was nearly identical in 1983 However, by 2001, the delinquent interest rate distribution has considerable mass to the right of the nondelinquent interest distribution (see bottom panel of Figure VII) This suggests that credit card interest rates have become more closely related to borrowers default risk Several recent papers document similar findings For example, Edelberg (2006) combines data from the PSID and the SCF, and finds that lenders have become better at identifying higher risk borrowers and have made increased use of risk-based pricing The timing coincides with the observation that in the late 1980s some credit card banks began to offer more different credit card plans “targeted at selected subsets of consumers, and many charge[d] lower interest rates” (Canner and Luckett 1992).26 5.2.3 Expansion of Credit to Lower Income Households In the model, financial innovations lead to an extension of credit to riskier borrowers We use SCF data to examine access to credit cards by income quintiles Not surprisingly, we find a strong positive relationship between credit card ownership and borrowing for all years However, the positive relationship between credit card ownership/borrowing and income in the SCF has become less pronounced in recent years For example, in 1983 only 11% (4%) of households in the lowest income quintile owned a credit card (carried a balance), versus 79% (37%) in the highest quintile This gap narrowed considerably during the 1990s By 2004, card ownership for the lowest income quintile more than tripled from 11% to 38% in 2004, while penetration for the top quintile increased to 96% This increase in access for lower income households has been accompanied by a significant increase in their share of total credit card debt outstanding Figure 6(c) plots the 26 Furletti and Ody (2006) report that credit card issuers also have made increased use of fees as ways to impose a higher price on riskier borrowers 27 cdf for the share of total credit card balances held by various percentiles of the earned income distribution in 1983 and 2004 The fraction of debt held by the bottom 30% (50%) of earners nearly doubled from 6.1% (16.8%) in 1983 to 11.2% (26.6%) in 2004 Given that the value of total credit card debt also increased, this implies that lower income households’ credit card debt increased significantly.27 To the extent that lower income groups are riskier, these findings suggest that borrowing by riskier households has increased over the past two decades Conclusion This paper develops a qualitative incomplete markets model to explore the effect of financial innovations on unsecured consumer credit markets This allows us to derive predictions for how commonly discussed financial innovations, based on improved information technology, impacts equilibrium credit contracts, borrowing, and defaults To evaluate these predictions, we assemble cross-sectional data on credit card interest rates and the distribution of credit card borrowing over the past thirty years Our findings support the view that financial innovations (likely due to improvements in information technology) in the credit card market played a key role in the rise in unsecured borrowing and bankruptcies over the past thirty years Our model predicts that financial innovations lead to more credit contracts, with each contract targeted at smaller groups, and the extension of credit to riskier households As a result, financial innovations lead to higher aggregate borrowing and defaults We find that these predictions are surprisingly consistent with changes in the aggregate and cross-sectional pattern of borrowing and defaults in the U.S over the past twenty-five years The model implies that interpretations of the unsecured credit market using a “standard” competitive framework 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Economics 90:629–650 Sanchez, Juan 2010 The IT Revolution and the Unsecured Credit Market Federal Reserve Bank of St Louis Working Paper 2010-022A WP 2010-022A Siddiqi, Naeem 2006 Credit Risk Scorecards – Developing and Implementing Intelligent Credit Scoring Hoboken, New Jersey: John Wiley & Sons, Inc Tufano, Peter 2003 “Financial Innovation.” Chapter of Handbook of the Economics of Finance, edited by G.M Constantinides, M Harris, and R Stulz, 307–335 Elsevier B.V White, Michelle 2007 “Bankruptcy Reform and Credit Cards.” Journal of Economic Perspectives 21:175–199 Wilson, C 1977 “A Model of Insurance Markets with Incomplete Information.” Journal of Economic Theory 16:167–207 A Verifying Equilibrium under Incomplete Information To verify that the allocation we have characterized is indeed an equilibrium, we need to check that a potential entrant cannot make positive profits by cream-skimming misclassified borrowers (by offering them (q ′ , L′ ) — a smaller risky loan with a better interest rate) The most profitable potential deviation makes the best customer indifferent between (q , L′ ) and the risk-free contract.28 Without loss of generality, u1 (q ′ , L′ ) = u1 (q, γyl ), which implies q−β ¯ L′ = ′ γyl (A.1) q −β ′ Equation (A.1) establishes a simple relation between q ′ and L′ The search for the most profitable deviation then amounts to searching over all possible q ′ A single smaller 28 Keeping the loan size fixed, any lower price would imply losing the best and most numerous customers, while any higher price would be leaving too much surplus to borrowers 33 risky loan may attract borrowers from a number of bins, and we thus have to calculate (and sum over) the profits generated from each of the equilibrium bins [σ n , σn−1 ), for n = 2, , N It is important to note that any contract that attracts misclassified borrowers necessarily disrupts the existing contract (into which these borrowers were misclassified) To see this, consider a contract (q ′ , L′ ) with L′ < γyh and q ′ > qn , which attracts borrowers with ρ′ > ρn Since ρ′ prefers this contract to the risk-free contract, so will ˆ every borrower with ρ < ρ′ , including ρn Since ρn is indifferent between the risk-free ˆ ˆ contract and (qn , γyh ), she strictly prefers (q ′ , L′ ) to the existing contract (qn , γyh ) Thus, for a given q ′ , and existing bin [σ n , σ n−1 ) served by (qn , γyh ), we have to consider two possible scenario First, the disruption to the existing contract may be small enough that the incumbent lender chooses not to exit the market This happens when incumbent’s profit loss is smaller than χ Second, if the profit loss from losing the best (misclassified) customers is larger than χ, the incumbent lender will exit Anticipating ′ this scenario, the entrant offers a replacement contract (qn , γyh ) to (correctly labeled) customers with σ ∈ [σ n , σn−1 ) in order to prevent them from applying for the (q ′ , L′ ) contract, which would make it unprofitable If the entrant is unable to offer such a replacement contract, the entrant will avoid dealing with the bin [σ n , σ n−1 ) by setting the eligibility requirement of the (q ′ , L′ ) contract to σ = σ n−1 We provide the details of the numerical implementation in a separate web appendix B Data Appendix The Survey of Consumer Finance questions on the credit card interest rate of respondents for 1995 - 2004 were for the card with the largest balance, while the 1983 survey asked for the average annualized interest on the bank or store card used most often if the full amount was not paid When counting the number of different interest rates, we drop imputed values The sample size increases, but by much less than the reported number of different interest rates (see the online appendix for the sample size by year) In Figure 6(c), earned income is Wages + Salaries + Professional Practice, Business, Limited Partnership, Farm + Unemployment or Worker’s Compensation Figures 6(a) and 6(b) are based on surveys asking banks about interest rates charged to consumers administered by the Board of Governors The 24-months consumer loans series is from the Quarterly Report of Interest Rates on Selected Direct Consumer Installment 34 Loans (LIRS), and is available since February 1972 (coded as item LIRS7808) The survey asks for the most common (annual percentage) rate charged on “other loans for consumer goods and personal expenditures (24-month).” It includes loans for goods other than automobiles or mobile homes whether or not the loan is secured Home improvement loans and loans secured primarily by real estate are excluded The sample declines from 296 banks in 1972 to 100 in 2007 The credit card interest rate data is from the bi-annual (since 1990) Terms of Credit Card Plans (TCCP) We use series TCCP6258, including only nationally available plans Annual response rates range from 200 to 400 35 36 Figure II: Illustration of Equilibrium Contracts with Imperfect Information Figure I: Aggregate Facts Source: Livshits, MacGee, and Tertilt (2010) 5002 0002 5991 0991 5891 0891 5791 0791 000 ,1 rep sgniliF mocni l asopsi emo ni elb sopsid a c a c fo eg ne rep fo eg tne rep sa tiderc gni vlo veR t de eR 5 6 7 8 01 A) Number of Risky Contracts B) Length of Risky Contract Interval 0.035 80 0.03 60 0.025 0.02 40 0.015 0.01 20 Fixed Cost (χ) −4 −4 x 10 x 10 C) Fraction of Population with Risky Debt D) Total Risky Debt 0.46 0.25 0.44 0.24 0.42 0.23 0.4 −4 −4 x 10 x 10 E) Default Rates F) Interest Rates 0.2 0.8 Default/Population Max 0.6 0.15 Avg 0.4 Default/Borrower 0.1 0.2 Min −4 −4 x 10 x 10 H) Ex−Ante Expected Welfare G) Overhead Costs as Percent Borrowing 1.416 1.5 1.414 1.412 1.41 1.408 0.5 1.406 −4 −4 x 10 x 10 Figure III: Varying the Fixed Cost 37 B) Length of Risky Contract Interval A) Number of Risky Contracts −3 x 10 90 5.3 88 5.28 86 5.26 84 5.24 82 5.22 6 Risk−Free Rate C) Fraction of Population with Risky Debt D) Total Risky Debt 0.265 0.47 0.26 0.46 0.255 0.45 0.25 0.245 0.44 E) Default Rates F) Interest Rates 0.25 0.2 0.8 Default/Population Max 0.6 0.15 0.4 0.1 0.05 0.2 Default/Borrower Avg G) Overhead Costs as Percent Borrowing Min H) Ex−Ante Expected Welfare 1.425 0.255 1.42 0.254 1.415 0.253 1.41 0.252 1.405 0.251 1.4 Figure IV: Varying the Interest Rate 38 A) Number of Risky Contracts B) Length Risky Contract Interval 25 0.019 0.0185 20 0.018 0.0175 15 0.017 0.75 0.8 0.85 α 0.9 0.95 0.75 0.8 C) Fraction Population with Risky Debt 0.85 0.9 0.95 D) Total Risky Debt 0.24 0.4 0.22 0.2 0.35 Borr Elig 0.18 0.3 0.16 0.25 0.75 0.14 0.8 0.85 0.9 0.95 0.75 0.8 E) Default Rates 0.85 0.8 0.2 Max Default/Borrower 0.6 0.15 Avg 0.4 Default/Population 0.05 0.75 0.95 F) Interest Rates 0.25 0.1 0.9 Min 0.2 0.8 0.85 0.9 0.95 0.75 G) Overhead Costs as Percent Borrowing 0.8 0.8 0.85 0.9 0.95 H) Ex−Ante Expected Welfare 1.408 1.406 0.78 1.404 0.76 1.402 0.74 1.4 0.72 1.398 0.75 0.8 0.85 0.9 0.95 0.75 0.8 0.85 Figure V: Varying the signal accuracy 39 0.9 0.95 0.35 Coefficient of Variation 0.3 0.25 0.2 0.15 0.1 Credit card rates 24-month consumer loan rates 0.05 1971 1976 1981 1987 1992 1998 2003 (a) CV Consumer Interest Rates 03 5 52 5 02 02 02 02 02 02 51 51 51 51 51 01 5002 5002 5002 5002 0002 0002 0002 0002 0991 0991 0991 0991 0 0 5991 5991 5991 5991 (b) Average, Min and Max Interest Rate Across Banks 0.9 0.8 0.7 0.6 0.5 0.4 4002 4002 0.3 3891 0.2 0.1 0 10 20 30 40 50 60 70 80 90 100 (c) CDF Credit Card Borrowing vs Earned Income 40 Figure VI: Contract Variety, based on data from SCF, TCCP and LIRS 41 Figure VII: Histogram of Interest Rates for Delinquents vs Non-delinquents Source: Authors’ calculations based on SCF tneuqileD tneuqileD noN etaR tseretnI 0392827262524232221 20291 81 71 61 51 41 31 2111 01 1002 , aR r nI mar g o tsiH se t tse e t fo B tneuqileD 00.0 20.0 40.0 60.0 80.0 01 21 41 61 81 02.0 la Re ev t i eq Fr uen cy LEN AP tneuqileD noN etaR tseretnI 0392827262524232221 20291 81 71 61 51 41 31 2111 01 891 , aR r nI mar g o tsiH se t tse e t fo 00.0 01 02.0 03.0 04.0 05.0 06.0 la Re ev t i eq Fr uen cy A LEN AP ... Unsecured Credit.” Working Paper 08-06, Federal Reserve Bank of Richmond Working Paper Series Ausubel, Lawrence 1991 “The Failure of Competition in the Credit Card Market.” American Economic Review... with the Board of Governors interest rate data We thank the Economic Policy Research Institute, the Social Science and Humanities Research Council (Livshits, MacGee) and the National Science... Credit Markets e European Credit Research Institute Research Report No Rothshild, M., and J Stiglitz 1976 “Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information.”